The alternative to Georges Cuvier’s concept, that of severe and
sudden cooling, found enormous amplification in the rapidly emerging theory of
the ice age, and was promulgated by Louis
Agassiz, a young Swiss naturalist who started his career as Cuvier's assistant.
Agassiz reasoned that the extinct megafauna must have been tropical by nature
and they had probably been wiped out by the sudden arrival of a world-wide Siberian
winter, which stayed on to reign as the Great Ice Age:

"The gigantic quadrupeds, the Mastodons, Elephants, Tigers, Lions, Hyenas, Bears, whose remains are found in Europe from its southern promotories to the northernmost limits of Siberia and Scandinavia...may indeed be said to have possessed the earth in those days. But their reign was over. A sudden intense winter, that was also to last for ages, fell upon our globe; it spread over the very countries where these tropical animals had their homes, and so suddenly did it come upon them that they were embalmed beneath masses of snow and ice, without time even for the decay which follows death." (Agassiz, 1866, p. 208).

Agassiz's theory of mass extinction was based on his "discovery" of the "Great Ice Age" which he had vigorously defended toward doubting colleagues, ever since 1837 when he had first presented his ideas to the Swiss Society of Natural Sciences in Neuchâtel. The theory of a past ice age, which initially had been rejected by many leading geologists, was not new to many Alpine naturalists. But it was slow in gaining general acceptance by the profession, especially against the ingrained concept of the “Great Flood,” which could explain so many of the features Agassiz ascribed to ice action. Eventually, he won enough colleagues over by showing them the evidence in the field, especially the scratched surfaces of bedrock where rocks in the moving ice had gouged out deep marks before dumping them in a moraine.

While Agassiz's concept of the "Great Ice Age" brought him much fame, it turned out to hide a much more interesting and much more complicated story, as we shall see. It turns out the mammoth was not a tropical mammal, and was not wiped out by the Ice Age, but rather they evolved all throughout the ice ages, and became extinct at the end of the last one of these ice ages.

Before we look more closely at these relationships, let us pause to contemplate a possible consequence of the introduction of the concept of mass extinction by Cuvier, which was greatly elaborated on by Buckland with his theory of a “Great Flood.” Charles Lyell, the reigning doyen of geology, deeply disapproved of anything that looked like catastrophism. His point of view was "uniformitarian," preferring to explain the past as the product of now-observable, gradual causes. As for deluge events, he admitted “two principal sources of extraordinary inundation:” “First, the escape of the waters of a large lake raised far above the sea; and secondly, the pouring down of a marine current into lands depressed below the mean level of the ocean (Lyell, 1868).” Concerning extinctions, he preferred a theory of gradual elimination over sudden disappearance and emphasized subtle changes in climate, invasion by competing species, and overhunting by man. To explain the demise of the Siberian mammoth, whose remains are so abundant in places, he invoked increased seasonality.

Charles Darwin was strongly influenced by Lyell's views on the subject. Darwin saw extinction as a natural consequence of increased rarity. As long as we cannot explain abundance and rarity of organisms, he argued, we should not be surprised to be unable to explain extinction: “it is but rarity carried to the end" (Darwin, "Voyage of the Beagle", 1846). His search was thus for factors keeping abundance in check. From this search, we can easily imagine that Malthus' book on geometric population growth and limited food supply led him to the realization of a dynamic balance between the drive for expansion of a population and ecologic controls. There followed the additional insight that these controls should act selectively on the disadvantaged. In this scenario, Darwin's desire to help fight the catastrophist view of late Pleistocene extinctions ultimately led to the theory of natural selection .

Returning again to Agassiz's theory of the Great Ice Age, it was, strictly speaking, a figment of his imagination. It never happened the way he thought it did, as a sudden change from a tropical climate to a frozen world (with a return to warmer times more recently). Also, the onset of the Ice Age had nothing whatever to do with the extinction of the mammoth and the woolly rhinoceros. On the contrary: the giant mammals were creatures of the period of ice ages, not its victims. They died at the end of the last ice age, and their demise is one of the great remaining riddles of our past. Were humans responsible? Or was abrupt climate change to blame? Or a combination of both? What kinds of observations would one suggest to help solve this riddle? The one great idea that stood the test of time was Agassiz's insistence that there had been a lot of ice around not too long ago. This idea of ice ages emphasized that climate on Earth can change greatly, and it set the stage for climate reconstruction in Earth history.